Intro
Background Information: We were tasked by Kirk Bogard, the Associate Vice President for Development and External Relations at Miami University to explore a dataset of real student data in order to find relationships and patterns that he can use to give Miami a competitive advantage. After exploring the data, we found a few particular variables that can help us find a potential relationship in the dataset, survey_salary, survery_internships, and survey_state. We plan to build a regression model using the number of internships during college to predict salary after graduation, using state to control for salary. The purpose of this analysis is to provide information on the relationship between number of internships and salary information to FSB Career Services. This will help them give more accurate guidance to students to ensure they get the best full time opportunity for them.
Survey Overview: Usable Response %: Our initial dataset included information on much more than just internship and salary information, and as such there were observations that provided no meaningful information to our model. After removing these observations (e.g. those without a reported salary after graduation, unreported number of internships, unreported starting location), the dataset shrunk to a bit over 50% of the original size. Out of 3235 original observations, we were left with little over 1700 to work with.
Distribution of Number of Internships: To understand the data a bit better, we wanted to explore how many internships students were completing before going into the job force. According to this basic histogram, most students completed 1 or 2 internships, followed by 3, while 0,4, and 5 had fairly few instances. The distribution looks relatively normal, but seems to be skewed slightly right.
Internship Effects on Salary: Mean Salary by Number of Internships: This is a bar chart depicting the average salary after graduation grouped by the number of internships they completed. What we see from this graph is that salary increases a bit for each additional internship completed up to 3 internships, after which average salary levels out. We expected salary to generally increase after an additional internship is completed, and the chart seems to support this. However, it is interesting to see that having additional internships after completing 3 does not seem to have an effect on salary, even lowering expected salary with 5 internships (potentially due to there being so few observations with 5 internships). This could indicate you do not need more than 3 internships if you want to maximize salary after graduation.
Regression Model Predicting Salary by Number of Internships:
Using a regression model we predicted salary by number of internships using 0 internships as a baseline.
Having 1 internship increases the predicted salary by $3605 compared to 0 internships
Having 2 internships increases the predicted salary by $5838 compared to 0 internships
Having 3 internships increases the predicted salary by $7542 compared to 0 internships
Having 4 internships increases the predicted salary by $7506 compared to 0 internships
Having 5 internships increases the predicted salary by $7553 compared to 0 internships, however this is not a significant predictor for salary
There is a sizable increase in salary when adding another internship up until 3 internships, 4 internships is a slight decrease from 3 internships and 5 internships is about the same as 3 and 4, but it is not a significant predictor.
Survey Overview
Overview of survey responses
row
Usable Response %
Usable Responses
1725row
Distribution of Number of Internships
Internship Effects on Salary
Column
Mean Salary by Number of Internships
Column
Regression Model Predicting Salary by Control Variables
Call:
lm(formula = formula_control, data = df)
Residuals:
Min 1Q Median 3Q Max
-38747 -6310 -332 5899 108835
Coefficients:
Estimate Std. Error t value
(Intercept) 49588.280 8391.856 5.909
survey_stateIL 4122.531 646.687 6.375
survey_stateOther 4455.649 654.219 6.811
survey_stateUnknown 3359.317 1364.012 2.463
major1Business Analytics 6636.994 2011.416 3.300
major1Business Economics 3170.312 1453.012 2.182
major1Entrepreneurship -5333.738 3238.323 -1.647
major1Finance 3389.686 885.634 3.827
major1Human Capital Mgmt& Leadership -4247.507 1851.485 -2.294
major1Information Systems 7599.443 1376.562 5.521
major1Management and Leadership -3130.762 2119.192 -1.477
major1Marketing -5459.029 940.453 -5.805
major1Supply Chain & Operations Mgmt 47.551 1151.406 0.041
`Combined Bacc and Masters` -971.754 1169.298 -0.831
`Dean's List` -748.616 696.333 -1.075
`First Generation College Stdnt` -843.117 1025.153 -0.822
`FSB Scholars` 934.737 1759.242 0.531
`Honors Program` 1279.472 1897.256 0.674
`President's List` 67.974 1365.768 0.050
`Cum Laude` 4721.870 2395.703 1.971
`Magna Cum Laude` 6037.442 2572.600 2.347
`Summa Cum Laude` 9135.325 2730.274 3.346
`University Honors` -767.161 2072.027 -0.370
`UniversityHonors w/Distinction` -1855.295 3917.603 -0.474
minor1Arts Related -5919.015 2248.640 -2.632
minor1Business Analytics -990.745 1960.587 -0.505
minor1Business Legal Studies -5270.065 5683.975 -0.927
minor1Economics -3898.320 2835.311 -1.375
minor1Education -6048.032 7830.299 -0.772
minor1Engineering/Science 626.980 2709.195 0.231
minor1Entrepreneurship 499.853 2596.750 0.192
minor1Health Related -10084.253 11047.638 -0.913
minor1Humanities -1173.819 2017.328 -0.582
minor1Information Security 1386.937 3335.584 0.416
minor1Information Systems 1105.064 2158.897 0.512
minor1Interactive Media Studies 8.363 2258.877 0.004
minor1International Business -2974.845 3593.633 -0.828
minor1Language -2337.604 2129.496 -1.098
minor1Mangement and Leadership -1689.472 2204.826 -0.766
minor1Marketing -2331.236 2822.045 -0.826
minor1Math/Stat -30.826 4091.193 -0.008
minor1Media Related 1702.977 4238.460 0.402
minor1No Minor -974.393 1783.141 -0.546
minor1Political Science 2119.806 3073.955 0.690
minor1Sport Management -2486.016 2510.684 -0.990
minor1Supply Chain Management -501.174 2535.387 -0.198
IPEDS.Race.EthnicityAsian -1425.230 7788.050 -0.183
IPEDS.Race.EthnicityBlack or African American 3445.704 8001.449 0.431
IPEDS.Race.EthnicityHispanic/Latino -1987.979 7730.110 -0.257
IPEDS.Race.EthnicityMulti Racial -2349.612 7773.044 -0.302
IPEDS.Race.EthnicityNon-Resident Alien -3831.434 7974.649 -0.480
IPEDS.Race.EthnicityUnknown -1256.635 9373.964 -0.134
IPEDS.Race.EthnicityWhite -3604.573 7631.910 -0.472
GenderMale -453.290 579.518 -0.782
GPA.Range2.50 - 2.99 5074.447 2944.495 1.723
GPA.Range3.00 - 3.49 9010.521 2841.992 3.170
GPA.Range3.50 - 4.00 8059.228 3755.374 2.146
Pr(>|t|)
(Intercept) 4.16e-09 ***
survey_stateIL 2.36e-10 ***
survey_stateOther 1.35e-11 ***
survey_stateUnknown 0.013885 *
major1Business Analytics 0.000988 ***
major1Business Economics 0.029257 *
major1Entrepreneurship 0.099732 .
major1Finance 0.000134 ***
major1Human Capital Mgmt& Leadership 0.021908 *
major1Information Systems 3.91e-08 ***
major1Management and Leadership 0.139774
major1Marketing 7.70e-09 ***
major1Supply Chain & Operations Mgmt 0.967063
`Combined Bacc and Masters` 0.406060
`Dean's List` 0.282493
`First Generation College Stdnt` 0.410950
`FSB Scholars` 0.595261
`Honors Program` 0.500163
`President's List` 0.960312
`Cum Laude` 0.048892 *
`Magna Cum Laude` 0.019051 *
`Summa Cum Laude` 0.000838 ***
`University Honors` 0.711246
`UniversityHonors w/Distinction` 0.635862
minor1Arts Related 0.008560 **
minor1Business Analytics 0.613393
minor1Business Legal Studies 0.353967
minor1Economics 0.169342
minor1Education 0.439994
minor1Engineering/Science 0.817012
minor1Entrepreneurship 0.847380
minor1Health Related 0.361481
minor1Humanities 0.560734
minor1Information Security 0.677610
minor1Information Systems 0.608813
minor1Interactive Media Studies 0.997047
minor1International Business 0.407897
minor1Language 0.272482
minor1Mangement and Leadership 0.443629
minor1Marketing 0.408877
minor1Math/Stat 0.993989
minor1Media Related 0.687889
minor1No Minor 0.584831
minor1Political Science 0.490540
minor1Sport Management 0.322232
minor1Supply Chain Management 0.843326
IPEDS.Race.EthnicityAsian 0.854819
IPEDS.Race.EthnicityBlack or African American 0.666789
IPEDS.Race.EthnicityHispanic/Latino 0.797077
IPEDS.Race.EthnicityMulti Racial 0.762479
IPEDS.Race.EthnicityNon-Resident Alien 0.630969
IPEDS.Race.EthnicityUnknown 0.893375
IPEDS.Race.EthnicityWhite 0.636772
GenderMale 0.434218
GPA.Range2.50 - 2.99 0.085007 .
GPA.Range3.00 - 3.49 0.001549 **
GPA.Range3.50 - 4.00 0.032013 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10740 on 1668 degrees of freedom
Multiple R-squared: 0.2218, Adjusted R-squared: 0.1957
F-statistic: 8.491 on 56 and 1668 DF, p-value: < 2.2e-16Column
Regression Model Predicting Salary by Internships
Call:
lm(formula = formula_interest, data = df)
Residuals:
Min 1Q Median 3Q Max
-40735 -6125 -438 5528 108379
Coefficients:
Estimate Std. Error t value
(Intercept) 45656.640 8317.748 5.489
survey_internships1 3604.936 1011.826 3.563
survey_internships2 5837.802 1000.232 5.836
survey_internships3 7541.957 1140.991 6.610
survey_internships4 7406.342 2053.740 3.606
survey_internships5 7552.596 3926.439 1.924
survey_stateIL 3692.104 639.600 5.773
survey_stateOther 4219.424 644.808 6.544
survey_stateUnknown 3134.314 1344.771 2.331
major1Business Analytics 6045.129 1984.164 3.047
major1Business Economics 2887.437 1431.287 2.017
major1Entrepreneurship -6082.486 3209.615 -1.895
major1Finance 3010.297 875.810 3.437
major1Human Capital Mgmt& Leadership -4440.373 1822.688 -2.436
major1Information Systems 7222.134 1356.786 5.323
major1Management and Leadership -2306.465 2094.020 -1.101
major1Marketing -5749.178 929.134 -6.188
major1Supply Chain & Operations Mgmt 188.145 1136.568 0.166
`Combined Bacc and Masters` -825.223 1151.210 -0.717
`Dean's List` -672.548 685.842 -0.981
`First Generation College Stdnt` -509.133 1010.712 -0.504
`FSB Scholars` 500.544 1734.161 0.289
`Honors Program` 702.831 1869.680 0.376
`President's List` -6.991 1345.355 -0.005
`Cum Laude` 5045.039 2361.200 2.137
`Magna Cum Laude` 6306.967 2534.733 2.488
`Summa Cum Laude` 9180.678 2690.967 3.412
`University Honors` -405.174 2042.148 -0.198
`UniversityHonors w/Distinction` -1496.390 3877.650 -0.386
minor1Arts Related -6136.234 2214.978 -2.770
minor1Business Analytics -1396.087 1931.856 -0.723
minor1Business Legal Studies -7108.372 5600.846 -1.269
minor1Economics -4106.630 2792.557 -1.471
minor1Education -5229.608 7722.571 -0.677
minor1Engineering/Science 631.286 2671.908 0.236
minor1Entrepreneurship -646.780 2560.869 -0.253
minor1Health Related -9193.175 10877.860 -0.845
minor1Humanities -1246.316 1986.353 -0.627
minor1Information Security 610.528 3291.322 0.185
minor1Information Systems 687.629 2126.341 0.323
minor1Interactive Media Studies -517.292 2226.551 -0.232
minor1International Business -2984.491 3537.945 -0.844
minor1Language -2706.328 2097.039 -1.291
minor1Mangement and Leadership -1675.390 2172.781 -0.771
minor1Marketing -2967.478 2780.051 -1.067
minor1Math/Stat 671.404 4033.387 0.166
minor1Media Related 148.384 4203.460 0.035
minor1No Minor -1366.015 1757.372 -0.777
minor1Political Science 663.483 3039.468 0.218
minor1Sport Management -2971.458 2472.816 -1.202
minor1Supply Chain Management -1264.170 2497.980 -0.506
IPEDS.Race.EthnicityAsian -1408.696 7671.546 -0.184
IPEDS.Race.EthnicityBlack or African American 2739.443 7877.844 0.348
IPEDS.Race.EthnicityHispanic/Latino -2176.909 7610.957 -0.286
IPEDS.Race.EthnicityMulti Racial -2411.491 7653.818 -0.315
IPEDS.Race.EthnicityNon-Resident Alien -2744.629 7858.120 -0.349
IPEDS.Race.EthnicityUnknown -1261.634 9232.693 -0.137
IPEDS.Race.EthnicityWhite -3903.562 7514.445 -0.519
GenderMale -368.581 571.469 -0.645
GPA.Range2.50 - 2.99 5970.222 2901.606 2.058
GPA.Range3.00 - 3.49 9075.421 2799.000 3.242
GPA.Range3.50 - 4.00 7641.114 3697.900 2.066
Pr(>|t|)
(Intercept) 4.67e-08 ***
survey_internships1 0.000377 ***
survey_internships2 6.40e-09 ***
survey_internships3 5.16e-11 ***
survey_internships4 0.000320 ***
survey_internships5 0.054585 .
survey_stateIL 9.30e-09 ***
survey_stateOther 7.97e-11 ***
survey_stateUnknown 0.019886 *
major1Business Analytics 0.002350 **
major1Business Economics 0.043817 *
major1Entrepreneurship 0.058255 .
major1Finance 0.000602 ***
major1Human Capital Mgmt& Leadership 0.014948 *
major1Information Systems 1.16e-07 ***
major1Management and Leadership 0.270859
major1Marketing 7.67e-10 ***
major1Supply Chain & Operations Mgmt 0.868541
`Combined Bacc and Masters` 0.473579
`Dean's List` 0.326924
`First Generation College Stdnt` 0.614513
`FSB Scholars` 0.772895
`Honors Program` 0.707032
`President's List` 0.995855
`Cum Laude` 0.032773 *
`Magna Cum Laude` 0.012936 *
`Summa Cum Laude` 0.000661 ***
`University Honors` 0.842752
`UniversityHonors w/Distinction` 0.699619
minor1Arts Related 0.005662 **
minor1Business Analytics 0.469987
minor1Business Legal Studies 0.204561
minor1Economics 0.141599
minor1Education 0.498383
minor1Engineering/Science 0.813254
minor1Entrepreneurship 0.800637
minor1Health Related 0.398161
minor1Humanities 0.530458
minor1Information Security 0.852863
minor1Information Systems 0.746444
minor1Interactive Media Studies 0.816311
minor1International Business 0.399033
minor1Language 0.197040
minor1Mangement and Leadership 0.440769
minor1Marketing 0.285938
minor1Math/Stat 0.867814
minor1Media Related 0.971844
minor1No Minor 0.437089
minor1Political Science 0.827231
minor1Sport Management 0.229671
minor1Supply Chain Management 0.612870
IPEDS.Race.EthnicityAsian 0.854329
IPEDS.Race.EthnicityBlack or African American 0.728079
IPEDS.Race.EthnicityHispanic/Latino 0.774896
IPEDS.Race.EthnicityMulti Racial 0.752748
IPEDS.Race.EthnicityNon-Resident Alien 0.726929
IPEDS.Race.EthnicityUnknown 0.891325
IPEDS.Race.EthnicityWhite 0.603499
GenderMale 0.519035
GPA.Range2.50 - 2.99 0.039788 *
GPA.Range3.00 - 3.49 0.001209 **
GPA.Range3.50 - 4.00 0.038951 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10570 on 1663 degrees of freedom
Multiple R-squared: 0.2484, Adjusted R-squared: 0.2208
F-statistic: 9.009 on 61 and 1663 DF, p-value: < 2.2e-16